# Thread: Percentage and fraction question

1. ## Percentage and fraction question

How do I turn 83 1/3 % into a fraction? I already have this:

83 and 1/3 divided by 100. I don't know what to do after that.

2. Originally Posted by ladyk
How do I turn 83 1/3 % into a fraction? I already have this:

83 and 1/3 divided by 100. I don't know what to do after that.
Apply basic arithmetic like this:

$\displaystyle 83\frac{1}{3}\div 100 = \frac{250}{3}\times\frac{1}{100}=\frac{250}{300}=\ frac{5}{6}$

3. Why would 83 1/3 % be changed to 250/3? That's what I'm having a hard time understanding.

4. Originally Posted by ladyk
Why would 83 1/3 % be changed to 250/3? That's what I'm having a hard time understanding.
So that you could multiply the fraction more easily and quicker. It would be just consist of more steps to multiply a fraction with a mixed fraction thats why it is changed to a top heavy fraction.

$\displaystyle \frac{250}{3}\times\frac{1}{100} = \frac{250 \times 1}{3 \times 100} = \frac{250}{300} = \frac{5}{6}$ < Completed in 4 Steps

$\displaystyle 83 \frac13 \times \frac{1}{100} = \left(\frac{83}{1} \times \frac{1}{100}\right) + \left( \frac{1}{3} \times \frac{1}{100}\right) = \left(\frac{83}{100}\right) + \left(\frac{1}{300}\right) =$ $\displaystyle \left(\frac{249}{300}\right) + \left(\frac{1}{300}\right) = \frac{250}{300} = \frac{5}{6}$ <Completed in 6 steps

Hence it is easier to multiply fraction by converting a mixed fraction to a top heavy fraction as it can be completed in less steps.

5. Ohhhh, thanks so much Air. I had no clue that 250/3 was just 83 and 1/3 % turned into an improper fraction. lol